Closure modeling for the conditional Reynolds stresses in turbulent premixed combustion

Abstract

Turbulence is significantly affected by combustion-induced dilatation in low Karlovitz number premixed flames. Conventional turbulence modeling approaches based on traditional unconditional averaging are limited in accurately capturing combustion heat release effects since they must capture both the direct influence of combustion heat release on turbulence and the flame dynamics. Solving momentum transport equations conditionally averaged with respect to a flame structure variable (progress variable for premixed combustion) could provide a superior framework for modeling combustion-affected turbulence since the flame dynamics are embedded into the flame structure variable conditioning. However, the conditional momentum equations contain numerous unclosed terms that evolve in both physical and phase spaces. Of the many unclosed terms, the conditional Reynolds stresses (conditional analog of the Reynolds stresses) represent the influence of turbulent transport on the conditional velocities. In this work, a new model consisting of two components for the conditional Reynolds stresses in turbulent premixed flames is developed to capture heat release effects on turbulence. The first component is the conditional analog of the Boussinesq model that characterizes turbulent shear effects in physical space. The second component depends on the conditional velocity gradient not in physical space but in phase space and captures the anisotropy in the conditional Reynolds stresses driven by thermal expansion effects that vary within the flame structure. The model is validated a priori using DNS databases of turbulent premixed jet flames at low and high Karlovitz numbers. At low Karlovitz number, the phase space term enables the model to capture direct heat release effects on all conditional Reynolds stress components, specifically the correct anisotropy of the normal components and the sign of the shear component. At high Karlovitz number where heat release effects on turbulence are insignificant, turbulent shear effects are dominant, and the phase space term has a nearly negligible effect.